You have a sliding puzzle that looks like this:

+---+---+---+---+
| A | B | C | D |
+---+---+---+---+
|   | E | F | G |
+---+---+---+---+
| H | I | J | K |
+---+---+---+---+

You may move a block with a letter on it to the blank space by sliding it there.

Determine the minimum number of moves it takes to put K where H is, J where I is, I where J is, and H where K is at the same time. (In other words, changing the configuration in row-3 from HIJK to KJIH.)

Note: The other pieces don't need to be in their original spots.